# Extensions 1→N→G→Q→1 with N=C23 and Q=S4

Direct product G=N×Q with N=C23 and Q=S4
dρLabelID
C23×S424C2^3xS4192,1537

Semidirect products G=N:Q with N=C23 and Q=S4
extensionφ:Q→Aut NdρLabelID
C231S4 = C24⋊D6φ: S4/C1S4 ⊆ Aut C2386+C2^3:1S4192,955
C232S4 = C23⋊S4φ: S4/C1S4 ⊆ Aut C2384+C2^3:2S4192,1493
C233S4 = C2×C22⋊S4φ: S4/C22S3 ⊆ Aut C23126+C2^3:3S4192,1538
C234S4 = C2×A4⋊D4φ: S4/A4C2 ⊆ Aut C2324C2^3:4S4192,1488

Non-split extensions G=N.Q with N=C23 and Q=S4
extensionφ:Q→Aut NdρLabelID
C23.1S4 = C24⋊Dic3φ: S4/C1S4 ⊆ Aut C231612+C2^3.1S4192,184
C23.2S4 = C42⋊Dic3φ: S4/C1S4 ⊆ Aut C231612+C2^3.2S4192,185
C23.3S4 = C42⋊D6φ: S4/C1S4 ⊆ Aut C23126+C2^3.3S4192,956
C23.4S4 = C23.S4φ: S4/C1S4 ⊆ Aut C23164C2^3.4S4192,1491
C23.5S4 = Q8.S4φ: S4/C1S4 ⊆ Aut C23164C2^3.5S4192,1492
C23.6S4 = Q82S4φ: S4/C1S4 ⊆ Aut C2384+C2^3.6S4192,1494
C23.7S4 = C23.7S4φ: S4/C22S3 ⊆ Aut C23246C2^3.7S4192,180
C23.8S4 = C23.8S4φ: S4/C22S3 ⊆ Aut C23246+C2^3.8S4192,181
C23.9S4 = C23.9S4φ: S4/C22S3 ⊆ Aut C23123C2^3.9S4192,182
C23.10S4 = C2×C42⋊S3φ: S4/C22S3 ⊆ Aut C23123C2^3.10S4192,944
C23.11S4 = Q8.1S4φ: S4/C22S3 ⊆ Aut C23486-C2^3.11S4192,1489
C23.12S4 = Q8⋊S4φ: S4/C22S3 ⊆ Aut C23246C2^3.12S4192,1490
C23.13S4 = C244Dic3φ: S4/C22S3 ⊆ Aut C23126+C2^3.13S4192,1495
C23.14S4 = C23.14S4φ: S4/A4C2 ⊆ Aut C2332C2^3.14S4192,978
C23.15S4 = C23.15S4φ: S4/A4C2 ⊆ Aut C2332C2^3.15S4192,979
C23.16S4 = C23.16S4φ: S4/A4C2 ⊆ Aut C2332C2^3.16S4192,980
C23.17S4 = C25.S3φ: S4/A4C2 ⊆ Aut C2324C2^3.17S4192,991
C23.18S4 = C2×Q8.D6φ: S4/A4C2 ⊆ Aut C2332C2^3.18S4192,1476
C23.19S4 = C2×Q8⋊Dic3central extension (φ=1)64C2^3.19S4192,977
C23.20S4 = C22×CSU2(𝔽3)central extension (φ=1)64C2^3.20S4192,1474
C23.21S4 = C22×GL2(𝔽3)central extension (φ=1)32C2^3.21S4192,1475
C23.22S4 = C22×A4⋊C4central extension (φ=1)48C2^3.22S4192,1487

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